How Do You Interpolate?

# How Do You Interpolate?

The simplest way to interpolate is by graphing the existing data points, drawing the best-fitting line and using linear interpolation to estimate a the value of a point for which there is no data available. Linear interpolation assumes that a line is the best fit for the data, but sometimes data points follow a curve that is better described using a polynomial.

In mathematics, the equation of a line is given by the formula y = mx + b. Mathematicians are able to determine the formula for a line with only two data points. Once the equation is determined, substituting any x value into the formula provides a y value. If the substituted x value lies between two known x values, the result is an interpolation. If the x value is outside the range of given x values, the resulting answer is an extrapolation.

When there are three or more data points, there are times that a curve provides a better fit than a line. While linear interpolation requires the line to pass directly through the two data points, curve-fitting interpolation requires the curve to match the existing data as closely as possible. Statisticians use different types of analysis to determine the interpolated value, including least squares analysis. Spreadsheet softwares, such as Excel, offers an easier method of interpolating data than calculations made by hand.

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